观察下列各式1/2=1/1x2=1/1-1/21/6=1/2x3=1/2-1/31/12=1/3x4=1/3-1/41/
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观察下列各式
1/2=1/1x2=1/1-1/2
1/6=1/2x3=1/2-1/3
1/12=1/3x4=1/3-1/4
1/20=1/4x5=1/4-1/5
1/30=1/5x6=1/5-1/6
.
请你猜想出(1)中的特点的一般规律,用含X(X表示整数)的等式表示出来
请利用上述规律计算(有过程)
1/2+1/6+1/12.+1/(n-1)n+1/n(n+1)
请利用上述规律,解方程
1/(x-4)(x-3)+1/(x-3)(x-2)+1/(x-2)(x-1)+1/(x-1)x+1/x(x+1)=1/x+1
原方程可以变形如下:
1/2=1/1x2=1/1-1/2
1/6=1/2x3=1/2-1/3
1/12=1/3x4=1/3-1/4
1/20=1/4x5=1/4-1/5
1/30=1/5x6=1/5-1/6
.
请你猜想出(1)中的特点的一般规律,用含X(X表示整数)的等式表示出来
请利用上述规律计算(有过程)
1/2+1/6+1/12.+1/(n-1)n+1/n(n+1)
请利用上述规律,解方程
1/(x-4)(x-3)+1/(x-3)(x-2)+1/(x-2)(x-1)+1/(x-1)x+1/x(x+1)=1/x+1
原方程可以变形如下:
![观察下列各式1/2=1/1x2=1/1-1/21/6=1/2x3=1/2-1/31/12=1/3x4=1/3-1/41/](/uploads/image/z/11524435-43-5.jpg?t=%E8%A7%82%E5%AF%9F%E4%B8%8B%E5%88%97%E5%90%84%E5%BC%8F1%2F2%3D1%2F1x2%3D1%2F1-1%2F21%2F6%3D1%2F2x3%3D1%2F2-1%2F31%2F12%3D1%2F3x4%3D1%2F3-1%2F41%2F)
1/2+1/6+1/12.+1/(n-1)n+1/n(n+1)
=1/1*2+1/2*3+1/3*4+...+1/(n-1)n+1/n(n+1)
=1-1/2+1/2-1/3+1/3-1/4+...+1/(n-1)-1/n+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)
1/(x-4)(x-3)+1/(x-3)(x-2)+1/(x-2)(x-1)+1/(x-1)x+1/x(x+1)=1/x+1
1/(x-4)-1/(x-3)+1/(x-3)-1/(x-2)+1/(x-2)-1/(x-1)+1/(x-1)-1/x+1/x-1/(x+1)=1/(x+1)
1/(x-4)-1/(x+1)=1/(x+1)
1/(x-4)=2/(x+1)
2x-8=x+1
x=9
=1/1*2+1/2*3+1/3*4+...+1/(n-1)n+1/n(n+1)
=1-1/2+1/2-1/3+1/3-1/4+...+1/(n-1)-1/n+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)
1/(x-4)(x-3)+1/(x-3)(x-2)+1/(x-2)(x-1)+1/(x-1)x+1/x(x+1)=1/x+1
1/(x-4)-1/(x-3)+1/(x-3)-1/(x-2)+1/(x-2)-1/(x-1)+1/(x-1)-1/x+1/x-1/(x+1)=1/(x+1)
1/(x-4)-1/(x+1)=1/(x+1)
1/(x-4)=2/(x+1)
2x-8=x+1
x=9
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观察下列各式1/2=1/1x2=1/1-1/21/6=1/2x3=1/2-1/31/12=1/3x4=1/3-1/41/
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